CODEWITHSUNDEEP
rregressionlinear-algebralinear-regression
Ems
Ems

Reputation: 1

poly() and orthogonal polynomials

I searched about poly() in R and I think it should produce orthogonal polynomials so when we use it in regression model like lm(y~poly(x,2)) the predictors are uncorrelated. However:

poly(1:3,2)=
[1,] -7.071068e-01  0.4082483
[2,] -7.850462e-17 -0.8164966
[3,]  7.071068e-01  0.4082483

I think this is probably a stupid question but what I don't understand is the column vectors of the result poly(1:3,2) does not have inner product zero? That is -7.07*0.40-7.85*(-0.82)+7.07*0.41=/ 0? so how is this uncorrelated predictors for regression?

Upvotes: 0

Views: 198

Answers (1)

Ben Bolker
Ben Bolker

Reputation: 226097

Your main problem is that you're missing the meaning of the e or "E notation": as commented by @MamounBenghezal above, fffeggg is shorthand for fff * 10^(ggg)

I get slightly different answers than you do (the difference is numerically trivial) because I'm running this on a different platform:

pp <- poly(1:3,2)
##                  1          2
## [1,] -7.071068e-01  0.4082483
## [2,]  4.350720e-18 -0.8164966
## [3,]  7.071068e-01  0.4082483

An easier format to see:

print(zapsmall(matrix(c(pp),3,2)),digits=3)
##        [,1]   [,2]
## [1,] -0.707  0.408
## [2,]  0.000 -0.816
## [3,]  0.707  0.408

sum(pp[,1]*pp[,2]) ## 5.196039e-17, effectively zero

Or to use your example, with the correct placement of decimal points:

-0.707*0.408-(7.85e-17)*(-0.82)+(0.707)*0.408
## [1] 5.551115e-17

Upvotes: 3

Related Questions